Industry, worldwide, discharges over 100×1012 joules (TJ) annually of low-grade waste heat (10° C. to 250° C.) from electric power stations, pulp and paper mills, steel and other metal foundries, glass manufacturers and petrochemical plants. A technology to recover or convert this low-grade waste heat to usable electricity could save industrial sectors tens of millions of dollars annually, through increased process efficiencies and reduced fuel costs, while substantially reducing greenhouse gas emissions. Other opportunities also exist for active cooling and electrical power generation for sensor systems on much smaller scales, such as on-chip active heat sinks, concentrated photovoltaic solar cells, and in standalone computers systems and computer data processing centers.
The useful work content of all thermal engines is thermodynamically limited by the Carnot efficiency, ηCarnot:ηCarnot=1−TL/TH  (1)where TH is the temperature of the heat source and TL is the temperature of the heat sink.
Thermal energy gradient power generators convert heat (Qin) into electrical energy (Wout) with efficiency:η=Wout/Qin=(WE−WP)/(CvΔT+QInt+QLeak)  (2)where WE is the generated electrical energy, WP is the energy lost in the temperature cycle, Cv is the heat capacity of the pyroelectric device, QInt are the intrinsic heat losses in the thermal cycle and QLeak are the heat leakages between the hot and cold sources.
Presently contemplated thermal to electrical energy conversion techniques (thermoelectric, piezoelectric and pyroelectric) all suffer from low energy conversion efficiencies, limited partly by the Carnot efficiency, but also by the inherent limitations of the conversion technologies themselves. Pyroelectric converters remain relatively unexplored, as early attempts to model and fabricate converters based on pyroelectric operating principles gave uneconomically low conversion efficiencies (0.1-2%). Other modeling studies were much more encouraging however, with overall predicted energy efficiencies ranging from 10 to 40% and with Carnot efficiencies in the range 50-80% or higher. In contrast, thermoelectric generators have maximum Carnot efficiencies around 14-17% and overall maximum efficiencies around 5%.
Traditional quasi-thermal pyroelectric energy generators rely on the property that the spontaneous polarization (and hence dielectric constant) of certain materials is temperature dependent. Cycling the material's temperature induces an alternating current in an external circuit when the pyroelectric material is made the dielectric in a capacitor. This property is shown schematically in FIGS. 1A-1C, where the intrinsic dipole moment of the pyroelectric material is made part of a capacitor and an ammeter is connected between the two capacitor electrodes. As shown in FIG. 1B, at constant temperature, no current flows in the circuit. When the capacitor temperature is increased, as shown in FIG. 1C, the polarization PS decreases, effectively reducing the capacitor's dielectric constant, and causing a current to flow in the external circuit to compensate for the decrease in the bound charge in the capacitor. This property can be used to generate electricity where the electrical current and energy conversion efficiency depends on the rate of change, and on the magnitude of the temperature change in the capacitor.
The quasi-isothermal cycle used in the simple prior art energy harvester shown in FIGS. 1A-1C is very inefficient and, as a result, produces very little power. However, by allowing large temperature swings across the device, and by placing alternating voltages on the electrodes of the pyroelectric capacitor as indicated in FIG. 2, much higher efficiencies and output powers are achievable. This cycle is known as an Ericson thermal energy generation cycle and has been used in previous attempts to generate electricity from thermal energy gradients. Other thermal cycles include Rankin and Stirling cycles and are used in steam power plants, internal combustion engines and refrigerators.
The cycle starts at (a) in FIG. 2 with the pyroelectric capacitor at low temperature TL and the ferroelectric capacitor charged at high voltage V2. As the temperature increases to TH at a constant applied voltage (b), charge is forced to flow in the external circuit charging the storage capacitor, such as in an embodiment shown in FIG. 8. The applied voltage is then reduced to V1 at (c) and the temperature of the pyroelectric capacitor decreased to TL again (d), producing another, opposite sign, current flow in the external circuit.
The pyroelectric current Ip produced during the cycle shown in FIG. 2 is:IP=Af(dPs/dt)=Afp(dT/dt)  (3)where Af is the surface area of the pyroelectric thin film capacitor, PS (C/m2) is the pyroelectric thin film polarization, such as in the embodiment shown in FIG. 1, T is the pyroelectric capacitor temperature and p is the pyroelectric coefficient in C/m2K. The net output power Np from the pyroelectric capacitor is:Np=VapplIp=VapplpAf(dT/dt)  (4)where Vappl is the external applied voltage across the pyroelectric capacitor, such as in an embodiment shown in FIG. 3. The cumulative pyroelectric conversion output work Wout from the cycle is as follows:Wout=Vappldq=∫Npdt=∫VapplpAf(dT/dt)dt  (5)
Equation 5 is shown schematically in FIG. 2 where Wout is the integral over the area within the figure: the greater the change in applied voltage across the pyroelectric capacitor and the wider the temperature swing, the larger the amount of heat energy converted to useful electrical energy. Equations 3 and 5 also show that the magnitude of the current and electrical energy generated by this circuit is also dependent on the magnitude of the pyroelectric coefficient p, the size of the capacitor (plate area A), and very importantly, on the rate of change in the temperature across the pyroelectric capacitor. Hence the faster the temperature can be cycled back and forth across the device, the more efficient the energy conversion process is and the greater the amount of electrical energy generated.
Prior attempts to use this technique to generate electricity have suffered from low energy conversion efficiencies due to the low operating frequencies (<1 Hz), large power requirements to generate significant temperature cycles (Wp in Equation 1), large thermal mass capacitor systems with relatively low breakdown strengths (i.e. low voltage differences, V2−V1) and low thermal conductivities (leading to low ΔT/Δt) and hence low ΔQ/ΔT.